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D O C U M E N T O D E T R A B A J O
Instituto de EconomíaDO
CUMENTO
de TRABAJOI N S T I T U T O D E E C O N O M Í A
www.economia.puc.cl • ISSN (edición impresa) 0716-7334 • ISSN (edición electrónica) 0717-7593
Sudden Stops in Social Mobility:Intergenerational Mobility in Chile
Claudio Sapelli.
4002011
Versión impresa ISSN: 0716-7334
Versión electrónica ISSN: 0717-7593
PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE
INSTITUTO DE ECONOMIA
Oficina de Publicaciones
Casilla 76, Correo 17, Santiago
www.economia.puc.cl
SUDDEN STOPS IN SOCIAL MOBILITY: INTERGENERATIONAL
MOBILITY IN CHILE Claudio Sapelli*
Documento de Trabajo Nº 400
Santiago, Noviembre 2011
INDEX
ABSTRACT 2
I. INTRODUCTION 3
II. LITERATURE REVIEW 5
III. FRAMEWORK 8
IV. DATA AND EMPIRICAL STRATEGY 12
IV.1 Data sources 12
IV.2 Empirical Strategy 13
V. INTERGENERATIONAL MOBILITY OF EDUCATION BY COHORTS 14
VI. HOW CAN WE EXPLAIN THE STAGNATION IN MOBILITY? 15
VI.1 Hypotheses 15
a. Human capital accumulation 15
b. The supply side 17
VI.2 Estimation results 20
VI.3 The combined effect of supply and demand factors 21
VII. THE MAIN CHANNEL: EDUCATIONAL ATTAINMENT OF CHILDREN ACCORDING TO
PARENTS’ ATTAINMENT 22
VII.1 Absolute coverage 22
VII.2 Coverage according to parents’ attainment 24
VIII. CONCLUSIONS 26
REFERENCES 28
APPENDIX 1 31
A1.1 Family structure 31
A1.2 Mandatory schooling laws 33
1
SUDDEN STOPS
IN SOCIAL MOBILITY:
INTERGENERATIONAL MOBILITY
IN CHILE
Claudio Sapelli*
Economics Department
Pontificia Universidad Católica de Chile
THIS VERSION: October 2011
*I would like to thank Pilar Alcalde for her outstanding assistance and her exceptional dedication.
Jorge Cariola helped to complete the task very efficiently. I would also like to thank the comments
and suggestions received at the internal workshop of the Economics Department at the PUC and at
the Meetings of the Chilean Economist Society 2007 and 2008.
2
SUDDEN STOPS IN SOCIAL MOBILITY:
EXPLAINING THE EVOLUTION OF THE
INTERGENERATIONAL MOBILITY OF EDUCATION IN
CHILE BY COHORTS
Claudio Sapelli*
Economics Department
Pontificia Universidad Católica de Chile
ABSTRACT
We estimate the evolution of intergenerational mobility of education in Chile for synthetic
cohorts born between 1930 and 1978. The correlation coefficient between children and
parent education falls from 0.67 for the cohort born in 1930 to 0.41 for that born in 1956, a
process of improvement that suddenly stops, followed by stagnation. We find that the
stagnation is explained by the effect on tertiary education coverage of low incomes when
the children were born (long-run credit constraints) and the restrictions to the supply side
of tertiary education (that had a particularly strong effect on children from less educated
parents) during the late seventies and early eighties.
Keywords: Intergenerational mobility, Synthetic cohorts, Education
JEL Classifications: J62, I20
3
I. Introduction
Up until now sudden stops had been studied in macro papers as a consequence of a crisis.
In this paper we detect permanent social effects from fiscal crisis and other macro events.
We examine the evolution of intergenerational mobility of education in Chile for cohorts
born between 1930 and 1978, which went through the educational system between 1936
and 2002. The key conclusion is that mobility significantly improved, and reached levels
that could be considered high in international comparison, for those cohorts born from the
mid-fifties onwards. However, after that, the process of improvement suddenly stopped and
mobility stagnated for many years (up to the end of the period we study).
To measure mobility we estimate the regression coefficient of parent's education on
children's education. We then analyze the causes behind the evolution we uncover. We
study the factors that explain the improvement in mobility, but we put emphasize in
understanding the stagnation that followed. We find that two factors explain the stagnation.
First, the effect on tertiary education coverage of low parental incomes when the children
were born (long-run credit constraints) and second, the restrictions on the supply side of
tertiary education coverage produced by the fiscal crisis that occurred in the mid-seventies
and early eighties (particularly relevant for children of less educated parents). We explain
both findings in greater detail below.
Through testing different hypothesis we find that the stagnation of mobility of education is
due to the difficulty of certain groups to access tertiary education. In turn, this is explained
by two factors. At least for the cohorts we study, access to tertiary education depends
strongly on family background. First, we find that one of the variables that explain the
evolution of the coverage of tertiary education is the income of parents when children were
born (referred as long-run credit constraints henceforth). Students whose parents had
relatively low incomes when they were born enter the educational system with a (relatively)
low level of human capital which makes future investments less productive, and since the
Chilean educational system is not able to make up for this handicap, these children arrive to
the end of high school with a low productivity of human capital investments. Hence tertiary
4
education may not be profitable for them, i.e. they may be better off with on-the-job
training.
The second element is the stagnation in tertiary education supply experienced by cohorts
born in 1956 onwards. This stagnation was motivated by the fiscal adjustment that occurred
in the mid-seventies and early eighties. Since tertiary education was mostly publicly funded
(and provided) the reduction in funding in effect resulted in a freeze in vacancies1. This was
an exogenous change, not motivated by any demand-side factors. Even though children
may have had the necessary abilities to access tertiary education, they were not able to do it
due to capacity constraints, making the process of increasing mobility stop2. The rationing
was done by the academic aptitude test, in which student‟s performance is highly
influenced by the quality of their previous education.
To understand this process we examine the evolution of educational attainment, separating
the attainment of children according to their parent‟s educational level. We find that the
offsprings of adults with low levels of education (i.e. those only with primary education or
with some secondary schooling) present a very small increase in access to tertiary
education. In fact we observe a divergence in the evolution of their access to tertiary
education with respect to children of parents with more education. This divergence in
access is not observed in the access to primary or secondary education.
This is coherent with our two preferred hypothesis, since they would imply a negative
impact on the coverage of tertiary education for these children of less-educated parents. On
the one side these relatively less-educated groups are more exposed to long-run credit
constraints. Using data on wages for non-qualified workers, we find a period of stagnation
in long-term incomes (or estimated permanent incomes), which we show have a strong
relationship with both the mobility of education and tertiary education coverage for less-
educated parents.
1 At the time there was no procedure to open new tertiary education institutions.
2 In Appendix 2 we also test other hypothesis, such as mandatory education laws and family background.
Although some of them explain the pattern of mobility by themselves, when we interact them with long-run
credit constraints and supply stagnation they have no explicative power.
5
On the other side, regarding our second explanation, it is natural that the sons and daughters
of less-educated groups are those relatively closer to the margin of entrance to higher
education i.e. to the cutoff point in the academic aptitude test. When the total available
vacancies in tertiary education stagnated (actually they slightly decreased) those affected
were the sons of less-educated parents.
Our results pose an important challenge in terms of public policy. While the stagnation of
higher education supply ended around 1990, thus solving the supply-side issues, the greater
concern is related to early-childhood human capital investments and long-run credit
constraints3 4.
The rest of the paper is organized as follows. Section II discusses the relevant literature,
section III presents a brief theoretical framework of analysis, including the rationale for the
basic equations; section IV describes the data and presents some summary statistics and the
empirical strategy; section V presents the results of the empirical analysis for the evolution
of educational mobility; section VI tests several hypothesis to explain that evolution.
Section VI addresses the main channel for the stagnation, tertiary education coverage for
children of parents with different educational levels. Finally, section VII concludes.
II. Literature Review
Social mobility has become a widely studied phenomenon. Traditionally the literature has
used two ways to measure social mobility: mobility in education and income mobility.
Unfortunately, we need panel data to study these questions, and in most cases the data is
not available. This makes the study of mobility in developed countries a difficult task.
It would be useful to have results for both variables, since one could argue that they can
account for different elements of mobility, but to measure income mobility we need a
variable that does not exist – parent‟s permanent income –, and estimations with available
3 See also Cunha, Heckman, Lochner and Masterov (2006) for a complete review of the related literature.
Hidalgo and Urzúa (2010) argue that in Chile the effect of attendance to a PCC is positive and statistically
(and economically) significant and argue that public policy should be focused in the extension of coverage of
PCCs, especially for disadvantaged children. 4 See Cunha and Heckman (2007) for a model and results for developed countries.
6
data (such as parents education used as a proxy for parents income) are biased. The bias is
in the direction of finding that countries are less mobile than they actually are.
Researchers have preferred to estimate mobility in education, which can be thought as a
better approximation of permanent income for both parents and children. Mobility in
education has been largely studied in developed countries, especially the US (Spady (1967),
Bowles (1972), Hauser and Featherman (1976), and Blake (1985)), though other rich
nations also have been studied and compared (see Couch and Dune (1997) for the US and
Germany and de Broucker and Underwood (1998) for eleven developed nations5).
For the US, Mulligan (1997) estimates intergenerational elasticities in several variables,
including education. He finds relatively large differences between values of
intergenerational mobility for income, which shows a value of 0.43, earnings (i.e. wages)
and education (values of 0.34 and 0.29 respectively). Hertz et al. (2007) estimate the
persistence of educational levels using a 42 countries sample6. They find that the Latin
American countries occupy the top seven positions among the sample (ordered from less
mobile to more mobile), with an average correlation between parent and child education of
0.567, compared with 0.41 for Eastern bloc nations, 0.39 for Asian and developed countries
and 0.36 for the African sample.
There is a relatively high variation within Latin American countries in terms of mobility of
education. Behrman, Gaviria and Székely (2001), analyze household surveys taken mostly
during the 1990s in Brazil, Colombia, Mexico, Peru and the U.S.. They find that for the
entire population, the coefficient of correlation between parents and children education
ranges between 0.5 (Mexico and Peru) and 0.7 (Brazil). Additionally, they find an ongoing
process of higher mobility and larger educational coverage –with some stages of
deceleration or even reversion of the mobility process–. In their decomposition of the
population in cohorts, they show that both average schooling and mobility have risen for
Latin American countries. The correlation between parent‟s and children‟s education falls
5 The countries are: Australia, Belgium, Canada, Ireland, Netherlands, New Zealand, Poland, Sweden,
Switzerland and the UK. 6 The sample includes seven Latin American countries, eight countries from the “Eastern bloc” (former
communist economies), ten Asian nations, four African countries and 13 Western developed countries. 7 For Adults aged between 20 and 69.
7
from 0.8 to 0.5 in Brazil and Colombia, from 0.6 to 0.35 in Peru and from 0.6 to 0.45 in
Mexico. The Mexican pattern is confirmed by Binder and Woodruff (2002), who study the
evolution of the mobility of education during 47 years. They divide the sample into four
cohorts: those born between 1925 and 1944, between 1944 and 1955, between 1955 and
1964 and between 1965 and 1971 (cohorts 1 to 4 respectively). Their results show that
mobility increases (the correlation falls from 0.57 in cohort 1 to 0.42 in cohort 3, but then
raises to 0.5 in cohort 4). In general, empirical evidence for Latin America shows that
average schooling has grown through time, and this growth has been accompanied by an
improvement in mobility.
There are few studies of intergenerational mobility in Chile, and in general they have
investigated the evolution of income mobility, even though to do this they must “estimate”
parent‟s permanent income. The preference to estimate income mobility is curious since the
study of the mobility of education would not require the construction of any missing
variable (data is available from several sources). This literature uses parents‟ education to
estimate parents‟ income (see for example Núñez and Risco (2004) and Núñez and Miranda
(2006)) and hence their estimates are upward biased. This methodology uses a proxy for
parents‟ income8 in a regression between child‟s income and this proxy. As a consequence
the parameters will be inconsistent (i.e. overestimated) which will result in underestimating
mobility.
Núñez and Risco (2004) also estimate the mobility of education in terms of elasticities
using three different cohorts and find a fall in the coefficient (i.e. an improvement in
mobility) from 0.47 for those born between 1949 and 1961 to 0.32 for people born between
1969 and 1981. These latter results are highly comparable to ours, though we find that the
actual decrease in the regression coefficient is even larger.
Núñez and Miranda (2006) examine other studies that discuss the question about income
mobility, and present their own estimations using four different cohorts: those born in 1958,
8 They construct parent permanent income using a Two-Sample Instrumental Variables (2SIV) method. Using
one source which has income data available, they estimate a regression between income and a list of expected
“determinants”, such as education, job experience and occupation. Then, taking the coefficient of such
regressions, they predict father‟s income in the other sample, which now includes both parent and child
variables (but only child‟s income).
8
1967, 1977 and 1987. They cite Núñez and Risco (2004) and Contreras, Fuenzalida and
Núñez (2006), where child income elasticity with respect to parents income lies between
0.43 and 0.67, with a mean value of 0.55. They estimate the correlation of children and
parent´s education and find that, for the entire sample, it is 0.21, and falls from 0.37 for
those born between 1939 and 1949 to 0.15 for those born in 1970 and 1981. These latter
estimates are very low. Our results, though different in magnitude, have a similar trend.
Their results not only differ in magnitude with ours but with many others studies, for
example d‟Addio (2007) finds for a group of OECD countries levels that range from 0.28
(Australia and UK) to 0.45 (Ireland)9. While our results suggest that mobility of education
in Chile is very similar to OECD countries, Núñez and Miranda results would suggest that
mobility in Chile is significantly higher than in advanced economies.
III. Framework
The basic framework to study social mobility comes from the seminal paper by Becker and
Tomes (1986), which allows us to model the transmission of income, assets and
consumption from parents to children. If there are no credit constraints, parents invest in
human capital acquisition for their children, until the rate of return of this investment is
equal to the market rate. Under this scenario, parent‟s income is not relevant in the
determination of child‟s income, which is only determined by his innate skills, thus social
mobility is only determined by such abilities10
.
However, in the presence of market failures, specifically credit constraints, parents‟ income
turns into a determining factor in the educational level of their children. Thus the cost of
education is not only given by the market rate of return, but for the shadow cost of forgone
consumption. Credit constraints divide population into two groups, on the one side those
families which are not credit constrained; on the other, those who are credit constrained,
and make a suboptimal investment in human capital, which in turn results in higher income
persistence (i.e. lower mobility).
9 Sweden has a value of 0.30, while it is 0.34 for the US.
10 According to this model, the correlation cannot be zero, since it is at least determined by the transmission of
abilities and by the effect of these abilities over education and income (Grawe and Mulligan (2002)).
9
The general conclusion is that in presence of credit constraints mobility is lower in the
more constrained groups. It is important to point out that these groups are not necessarily at
the bottom part of the income distribution (Grawe and Mulligan (2002)); a group is
constrained when his optimal investment in education cannot be reached by his available
income. Then, if ability is positively correlated with income, the more constrained families
could counter-intuitively be in the upper part of the income distribution11
.
More formally, assume that each individual lives for two generations12
, the first represents
his childhood and the second his adulthood. Each individual has only one child. Suppose
that human capital in the generation is determined by investments made by parents ( ,
public expenditure ( ) and by endowments ( )13
:
( with (1)
A larger endowment usually raises the marginal benefit of both private and public
expenditures, so
(2)
With perfect access to capital markets the optimal investment in human capital will
equalize its marginal rate of return with the market interest rate
( (3)
With
⁄ ( ( . Let be the market interest rate in period , then
or ( (4)
At the optimum
11
Grawe and Mulligan (2002) and Núñez and Miranda (2006) find that mobility is higher in the bottom part
of the distribution rather than in the upper part, where persistence is larger. However Corak and Hiesz (1999)
argue that middle-class families are more credit constrained and present lower levels of mobility. 12
The model is based on Becker and Tomes (1986); see also Becker and Tomes (1979) and Bevan (1979). 13
Endowments can be thought as the heirloom from parents to children in terms of biological and cultural
elements that shape child‟s personality and behavior.
10
(by equation (3)), and (5)
This means that (i) parents whose children have larger endowments will invest more in
them, (ii) if the alternative cost of human capital raises, the optimal investment will fall,
and (iii) public and private investments are substitutes.
Replacing (4) into (1)
( ( ( (6)
With
And children better endowed will accumulate a larger amount of human capital.
But, what if not every family has full access to capital markets? To see this, imagine that
some parents cannot finance their optimal investment, and neither can access capital
markets fully. Parents must finance the investment by reducing consumption (theirs or their
children‟s), by selling assets or by raising labor supply (again, theirs or their children‟s).
This will make private expenditures dependant on not only endowments, public
investments and the interest rate as in equation (4), but also on parent‟s income. If income
is a function of human capital, then parent‟s education will influence the levels reached by
their children.
To see this suppose that
(7)
Where is income in period and represents “luck” (another way to express any
unsystematic variation in income). As optimal private investment in human capital now
depends on income, we can reformulate equation (4) as
( (8)
11
Replacing equation (7) in (8)
( (9)
And optimal investment will depend on parent‟s human capital. Putting (9) into (1)
( ( ( (10)
Where . The total derivates for , and (instead of ) have the same
sign, while now ⁄
⁄ and children from parents with higher human
capital will in turn accumulate a larger amount of it. Also assume that , so human
capital accumulation will converge up to some point14
.
Throughout the rest of the paper, we examine the evolution of intergenerational mobility of
education (i.e. the relationship between and ) by cohorts. We will see that the
relationship fell for those born in the first part of the XXth century (increasing mobility),
while it stagnated for cohorts born from the late-fifties onwards. We then test some possible
causes for this stagnation, and find that the stagnation of permanent income of less
educated parents and the stagnation of tertiary education supply are the main factors behind
the lack of access to the higher educational levels. Each explanation corresponds to one of
the factors the model predicts will affect human capital accumulation. First, since ,
the stagnation of parent‟s income during early childhood made the children of less educated
families lack the necessary resources to achieve their optimal level of schooling. Second,
the stagnation of higher education supply can be thought as decrease in public expenditure
in human capital. Although we know that the theoretical effect of this reduction is
ambiguous, since (see derivates after equation (6)), after the reduction in total
vacancies in universities, parents cannot substitute with private investment, so in fact
⁄
⁄ . These two effects (or the interaction of both) can explain the stagnation
in mobility of education for cohorts born in the latter part of the XXth century.
14
This convergence point could be different for different subgroups in the population. For example, some
group‟s convergence may be around complete secondary school (i.e. 12 years of education), though for other
may be complete higher education (17 or 18 years of education). See Sab and Smith (2002), and the
references they cite for evidence of convergence in human capital.
12
IV. Data and Empirical Strategy
IV.1. Data sources
We use data from the Encuesta de Protección Social (EPS) of 2002 and 200415
. We include
all cohorts born between 1930 and 1978 (in order to have enough mass on each cohort).
The EPS has questions related to the education of the parents (father and mother) and their
children. In total we have 73,493 data points.
To find actual rates of mobility, we first estimate a regression between the child of the
parent and his parents. We estimate using both educational levels and logs. This is what is
most frequently done in the literature to analyze mobility. Table 1 presents some summary
statistics of the number of observations by cohorts, along with the average schooling for
children and parents (the corresponding cohorts corresponds to the children year of birth).
The mean education by cohort almost doubled between those born in 1930 and the cohort
born in 1978, figure 1 shows this evolution. It increased from 6 years for the 1930 cohort to
11.7 for the generation from 1978. We can see two different stages in this evolution; first,
there is a sharp expansion of the mean between the cohorts born in 1930 and 1956. During
this first stage the average education for a cohort grew from 6 to 10 years (at a rate of
growth of 1.8% per year). For those cohorts born between 1958 and 1978 the rate of growth
was much slower (0.8%).
Another important feature of the data is that the difference between child‟s and parents‟
education for cohorts in the first period (1930-1956) starts at 1.5 years, and increases in the
middle part of the century, reaching a more-than-four-years difference for cohorts born
between 1956 and 1971; then it eventually starts to decrease (the difference in the 1978
cohort is 3.4 years). In the early part of the century the average schooling of new cohorts
started to diverge from the levels achieved by their parents, but due to factors that we will
15
We actually work with three different data sets, but only report here the results for one of them. The first
two data sets (the Encuesta de Caracterización Socio-Económica (CASEN) and the Encuesta de Movilidad
Social de Chile (EMSC)) do not have sufficient data by cohort and hence require the aggregation of different
cohorts to obtain statistically significant results. The third (the EPS) does allow us to work with each cohort
individually and it is these results that we report. The results with the three data sets follow very similar
patterns. We also study mobility of the child‟s education with respect to both the father‟s and the mother‟s
education, but only report here the results regarding the correlation with the father‟s education. This is
because when we include both parents‟ education in the regression, only the father‟s education is statistically
significant. In any case, results for the mother and the father are very similar.
13
examine later, this difference stopped increasing and then began to decrease for those born
in the second half of the century.
Someone could argue that this decrease in the difference is to be expected, since the years
of schooling are bounded from above. This may represent a problem only if the average
level of schooling is close to that bound, but this was not the case for those cohorts where
the difference began to decrease. The average schooling for the generation born in 1956 is
9.4 years, barely higher than complete primary education, thus a large space for growth was
still available.
Hence there must have been other factors that affected the educational level achieved by
these cohorts. In this paper we find that there are two crucial factors (and in other work we
discard another two). First, since we do not have information on permanent incomes for
parents to test the credit constraints hypothesis, we use the wages series for non-qualified
workers from Braun, Braun, Briones and Díaz (2000) as a proxy for current income for low
education parents. With this data we make several alternative estimates of permanent
income at the cohort-level16
.
Second, we use data for total enrolment in tertiary education from Díaz, Lüders and
Wagner (2010), who constructed the series for the entire history of Chile.
IV.2. Empirical Strategy
For the entire population we estimate:
(11)
Where represent the schooling of an individual from family and of the generation ,
where represents the children, while represents his parents. The schooling can
be measured in levels or in logs, in the latter case we will be measuring the
intergenerational elasticity. We expect that , and the closer to 0 is, the more
mobile the society is. But taking the entire population may confound different generations
that were educated in different environments, in terms of public policy and development.
16
Our preferred estimations use the 10-years average income of parents before the birth of the cohort as a
measure of permanent income. We also estimate 5- and 3-year averages, with highly similar results.
14
This is why it is useful to separate the population in cohorts, which we define as the sub-
group born in a specific year. We will then estimate:
(12)
Here the level of schooling from a child from family born in cohort has a correlation of
with his parent‟s. Also, is a cohort-specific constant (that controls for year-of-birth
effects). Also, under this specification we estimate a complete vector of , one for each
cohort.
Then, to test the different explanations we pose, we take the coefficient of parent‟s
education and run a regression of the form
(13)
Where the matrix contains the variables corresponding to each explanation. The specific
regressors included will be explained later17
.
V. Intergenerational mobility of education by cohorts
Figure 2 and table 2 show the intergenerational correlations of education, from a regression
of children´s years of education on the education of his father (equation 12). We ran
regressions both in levels and in logs and the results present the same trend (table 3 shows
the results of the regression in logs), we will concentrate only on the results in levels. The
evolution of the coefficient (in levels) graphed in figure 2 shows two stages. A first stage
for cohorts born between 1930 and 1957, in which the coefficient drops from 0.67 to 0.41
(a decrease in the dependence of the education of the child on the education of the father,
hence an increase in mobility). In a second stage from 1957 to 1978, the coefficient drops
only slightly and is practically constant. These stages coincide with the evolution of the
17
We ran the traditional Dickey-Fuller (D-F) test (see Dickey and Fuller (1979, 1981)) to test whether the
intergenerational mobility (i.e. the vector) corresponds to a stationary series. We did it in both levels and
logarithms. The only case where we are not able to reject at the 5% level the null hypothesis of unit-root is
when we test D-F for a random-walk without a drift or a time trend in the levels case (we reject the null for
five other cases: random walk with trend or drift in the levels regression and the three cases in the logs
regression).
15
average years of schooling, when the mean grew substantially mobility also increased.
Then, when the mean education grew more slowly, mobility stopped increasing18
.
While cohorts born in the first part of the sample (between 1930 and 1940) present
relatively low levels of mobility (higher levels of correlation), comparable with other Latin
American immobile countries, like Peru, Ecuador, Brazil, or Colombia; those born after the
forties show levels closer to those of the less mobile developed countries, like Italy. Finally,
the cohorts form 1957 onwards show levels comparable to more mobile countries, like the
US, or Sweden (Hertz et. al. (2007))19
.
VI. How can we explain the stagnation in mobility?
There are two main explanations for the “sudden-stop” in the evolution of mobility20
. That
is, for the difference in the evolution of mobility between cohorts born between 1930 and
1957, and generations born from 1958 onwards. The first is credit constraints (we test two
different margins as in Carneiro and Heckman 2002: credit constraints at birth and when
the decision to enter college is taken). This explanation focuses on the demand side of the
market, while the second focuses on supply factors. The second explanation is the freeze in
the supply of tertiary education that started in the mid-seventies (which affected entrance to
tertiary education of cohorts born in the late-fifties).
We find that these two variables, credit constraints at birth and the stagnation of tertiary
education supply in the seventies, are the two factors that best explain the stagnation of
intergenerational mobility of education.
VI.1. Hypotheses
a. Human capital accumulation
18
In terms of elasticities (regressions in logs, in table 3) the results are very similar, elasticity falls from 0.5 to
0.29 for the whole period. For the cohorts born between 1930 and 1957 the elasticity falls from 0.5 to 0.24;
for cohorts born between 1958 and 1978 the elasticity moves in a narrow range (between 0.26 and 0.29). 19
This comparison between correlations for cohorts in the case of Chile and for the whole population for the other countries is done for illustrative purposes only. 20
We also test two other hypotheses. First, since family composition has changed in Chile as it has changed in
developed countries, we test whether the increase in single parent families had effects on mobility. We find an
effect, though it vanishes when we control for the credit constraints hypothesis. Second, we test a command
explanation: we test for the effect of mandatory schooling laws. We find that minimum schooling laws did not
have any effect on the evolution of the intergenerational mobility of education. See Appendix 2 for details on
each hypothesis.
16
An argument that has gained weight among social and natural sciences says that the main
determinants of the achievement gap between groups in a society are differences in
investments in human capital in the first stages of life. According to this hypothesis the
accumulation of human capital in early childhood has a large impact on both cognitive (test
scores, IQ) and non-cognitive (motivation, perseverance, tenacity) skills.
At early stages of life the child‟s brain has still not completed its formation, thus there are
some areas susceptible to be shaped through different stimulus. The different stages of the
formation of human capital are highly complementary (see Heckman (2006), Heckman and
Masterov (2007), Doyle, Harmon, Heckman and Tremblay (2009)) thus the lack of early
investment will have a detrimental effect on the productivity of higher educational levels.
This explanation relates closely to the model proposed in section II, where, in the absence
of credit constraints, parents can endow their child with the optimal amount of human
capital. But if there are credit constraints, parents face a trade-off between child‟s education
and consumption. We need to discriminate between these two competing hypothesis in the
literature. The first is the argument found in Carneiro and Heckman (2002) (see also
Heckman (2006), Cunha, Heckman et al (2006), Doyle et. al (2009)) and says that, given
the dynamic complementarities of investments at different stages of life, if a child does not
receive the necessary stimulus in the early stages of his childhood, all investments made
later will have a lower return (e.g. see figure 2 in Doyle et. al (2009)). This is consistent
with long-run credit constraints, where the lack of necessary investments early in life hurts
the child‟s entire development path.
The second hypothesis is short-run or contemporaneous credit constraints (Card (1999,
2001), Cameron and Taber (2004)). Children from less educated parents may face credit
constraints for direct costs of schooling (monetary costs of tuition, books, transportation
and board and room), and for indirect costs of schooling (forgone earnings). We will refer
to this hypothesis as short-run credit constraints.
17
Although these two hypotheses are not mutually exclusive, there has been some debate in
the literature regarding the validity of each of them21
. We test whether the stagnation in
intergenerational mobility of education was driven by long- or short-run credit constraints,
if any.
Figure 3 shows the evolution of our measure of permanent income by cohort (see section
III.1), both short term (at 18) and long term (at birth). We estimate both series by the ten
year average of income before the year when the cohort reaches the respective age (birth or
18). We average the (real) income for low-skilled workers for the respective cohorts,
measured in thousands pesos.
Looking at both series we can see a marked divergence for cohorts born in the fifties, those
that were first affected by the stagnation. While contemporaneous permanent income
increases, permanent income at birth stays flat. Permanent income at birth begins to grow
for cohorts born in the early sixties, and this different path between long- and short-run
credit constraints may help us to discriminate between the two hypotheses competing to
explain the stagnation of mobility. It is this divergence we can exploit to determine which
of them affected access to education by children of low education parents. Since it is the
cohorts born in the fifties that are affected at first, if one of these two hypotheses has
explanatory power it looks like it should be income at birth. However, if it were so, that
explanatory power would run out for those cohorts born in the late sixties and beyond. So
we would need a complementary hypothesis to explain the persistence in the stagnation.
We find that in the supply side.
b. The supply side
The human capital accumulation decision is a choice made by families through an optimal
allocation of resources, taking supply conditions as given. Furthermore, models in this
literature such as Becker-Tomes assume that if a parent wants to buy one more unit of
human capital, it will be available. But this may not be the case, since governmental
21
For example, Carneiro and Heckman (2003) argue that “Conditioning on long term factors eliminates most
of the effect of family income in the adolescent years on college enrolment decisions for most people, except
for a small fraction of young people (p.709)”.
18
policies may arbitrarily expand or reduce the supply of vacancies in a certain educational
level. Therefore, we examine the effect of tertiary education supply on mobility.
Central to our analysis is the reduction in the higher education vacancies during the fiscal
crisis of the mid seventies (caused by the combination of a high fiscal deficit plus the
dramatic change in the terms of trade produced by the 1974 oil shock). Empirically, we find
that supply also played an important role in the stagnation of mobility. When we include
both hypotheses we find that it is long-run credit constraints together with the stagnation of
higher education supply that explains the interruption in the improvement of mobility.
Starting in 1967 there were pressures to increase vacancies in universities, channeled
through a movement denominated as “university reform” (see Brunner (1984), Brunner
(1986) Bernasconi and Rojas (2004)). It also sought to increase enrollment for children of
families with low incomes22
. Following up on these pressures, the government financed a
large increase in the supply of vacancies in universities23
. Public expenditure in tertiary
education almost doubled. Between 1967 and 1973 higher education enrolment grew from
56,000 to 140,000, an increase of 150% (see Díaz, Lüders and Wagner (2010)).
Starting in 1974 the government reduced sharply the supply of publicly funded vacancies in
higher education (along with a sharp reduction in real public expenditure, of between 15%
and 35%, depending on the CPI used to correct for inflation). Provision of private supply
was not possible until 1981, when the government introduced a new legal framework for
higher education24
. This reform authorized the opening of two new types of providers of
higher education: the Technical Formation Centers (TFC) and the Professional Institutes
(PI), and assigned to them the provision of non academic and technical degrees25
. While
TFCs were entrusted the provision of low-skilled professional degrees (for relatively low-
skilled white-collar occupations), PIs were assigned the provision of technical degrees (i.e.
22
As shown below, the difference between coverage of tertiary education between different groups was
relatively high in the sixties. For example, in 1965 only 7% children of parents with 6 or less years of
schooling were enrolled in higher education. 23
Before the reform of 1981 the only tertiary education institutions were universities, which had “the legal
monopoly over professional titles and academic degrees”. (Brunner (1984), p.8). 24
See Brunner (1984) (and his references), or Bernasconi and Rojas (2004) for a more detailed explanation of
the new reforms. 25
In fact there were some informal institutions of this type before the reform. This was precisely one of the
objectives of it: formalize and regulate these institutions which were giving informal education, and were not
subject to any control or regulation. We have no data of the supply of vacancies by these entities.
19
for blue-collar occupations, see Ministry of Education (1981b, 1981c)). Universities kept
the monopoly of professional degrees (for high-skilled white-collar occupations). A key
element of the new legal environment was that it created a framework in which new
universities could enter the market for the provision of professional degrees: “[t]he Ministry
of Education cannot deny the register of a university…” (see Ministry of Education
(1981a), Art.18°). However, during 1982-1989 there was almost no entrance of new
competitors in the universities‟ segment26
. This is strange, since there is evidence that there
were rents for potential entrants27
. What happened was that the new law established a
“double filter” for the creation of a new university. It had to be cleared both by the Ministry
of Education and the Ministry of Interior. The Ministry of Interior could deny entrance
when it judged the entrant threatened public order or national security (Ministry of
Education (1981a), Art.4°), and it is this filter that became binding.
Figure 4 shows the evolution of total tertiary education enrollment and the evolution for
each segment of the market. The evolution of total enrollment (the continuous line) shows
three different periods. First, it shows a period of continuous growth between the late
forties and the early seventies (with an average growth rate between 1948 and 1973 of
13%28
). The second period is from 1974 to 1981 (when the higher education reform
occurs), with an average decline rate of -2.0%. The third period goes from 1981 to the end
of the period analyzed, with an average growth rate of 8.1% a year.
A deeper look into the evolution of the different segments sheds some further light on what
happened. The reform marked a change in the structure of the tertiary market that cannot be
appreciated when looking at the series for total enrollment. We will refer to the period
before 1981 as the pre-reform period, and the period from then on as the post-reform
period. Total enrollment and universities‟ enrollment is identical in the pre-reform period
(by definition, since only universities participated in the market). In the post-reform period
26
Between these years only three universities entered in the market: Universidad Central, Universidad
Gabriela Mistral and Universidad Diego Portales. 27
Gallego (2010) shows an increase in the relative demand for skilled workers in the 1980s and 1990s, which
in turn should increase demand of tertiary education. This should have created positive rents in the market,
encouraging new entrants, which did not happen. 28
In fact this period contains two subperiods. The first is between 1948 and 1963, where the average growth
rate was relatively high (10.6%) and the post-reform period (from 1964 and 1973) where the rate of expansion
was even higher, with an average value of 16.9%.
20
the two series present very different behaviors. The biggest difference lies in the 1982-1989
period, in which total enrollment grows, while universities‟ enrollment remains practically
constant29
.
The hypothesis is that the stagnation of university enrollment is one of the principal reasons
behind the stagnation of mobility. Enrollment stopped growing in 1974, which coincides
exactly with the year of entrance to higher education of the cohort where the stagnation
began (i.e. 1956). The impossibility of further enrollment prevented many of them from
achieving a higher educational level, stagnating mobility.
VI.2. Estimation results
We estimate equation (13) allowing for different “versions” of the matrix . We test each
hypothesis separately, first including our measure of permanent income at birth and at age
18, to make both hypotheses “compete”. Then we test the “higher education hypothesis”
estimating the effect of university enrollment and total tertiary education enrollment.
Finally we test credit constraints and higher education jointly, allowing both demand and
supply factors to enter together.
Table 4 shows the results for the different hypotheses. In panel A, columns 1 and 2, we
estimate the effect of long- and short-run credit constraints separately, which show a very
similar impact, with a coefficient of around -0.003. Then, we regress both permanent
income at birth and at age 18 and find that short-run credit constraints “win”. That is, if we
include only demand-side factors, long-run credit constraints do not show a significant
effect on the evolution of intergenerational mobility. But as figure 3 shows, permanent
income at 18 began to raise and then fell before mobility stagnated, thus it cannot explain
both the improvement and the stagnation30
.
29
The respective growth rates are 9.4% for total and 1.7% for university enrollment. 30
We performed three different robustness checks for this result. First we estimate using the log of incomes
instead of levels (see columns 1 to 3 in table 9). Second we estimate using the intergenerational elasticity of
education as dependent variable (see columns 4 to 6 in table 9). Finally we use a different definition of
permanent income; we average 5 (instead of 10) lags of low-skilled workers wages (see table 10). Overall,
tables 4 (panel A), 9 and 10 tell us that (i) income is an important determinant of intergenerational mobility of
education, and (ii) the measure of income that we choose matters, since while incomes at birth and age 18 for
generations born before the fifties decade were highly similar, for those born on the early fifties and after
21
Panel B in table 4 explores the effect of the evolution of higher education supply on the
mobility of education. Here we can also see some interesting patterns. As we saw that in the
post-reform period the universities and total tertiary-education supplies behave very
differently, we estimate using both series separately. Column 1 uses enrollment only in
universities, while column 2 uses total tertiary enrollment and column 3 also uses total
enrollment but disaggregated by type of institution (universities, TFCs and PIs). The results
are robust to the use of logs instead of levels of supply, see table 11.
Higher education supply had a positive and significant effect on mobility (this is true for
both universities and total supply). What may seem surprising is that the separate effect of
PIs and TFCs is not significant, when we would expect that the possibility of achieving less
skilled tertiary degrees would be a preferred option for some families, which should
improve mobility31
. In the next section we will combine both demand and supply factors in
our empirical work.
VI.3. The combined effect of supply and demand factors
Here we estimate the combined effect of permanent income at birth, at age 18 and the
supply of tertiary education on intergenerational mobility. Table 5 shows the results.
The results from table 4 are confirmed by this “combined” estimation. Tertiary education
enrollment measured both as universities‟ and total enrollment show a robust and positive
effect on mobility. The mobility improvement during the entire period was 0.262 (see table
2) while the total expansion of universities supply was 236,523. Using the coefficient in
column 1, table 5, we see that universities‟ enrollment by itself predicts a reduction of
0.227 in intergenerational mobility, 86% of the total actual reduction. The coefficient of
universities supply remains constant across the three different specifications in columns 1
to 3, which is evidence that independently of credit constraints, the expansion of tertiary
education was an important factor in the process of improvement and stagnation of
intergenerational mobility.
permanent incomes for low-skilled workers stagnated (specially incomes at birth), which in turn contributed
to the stagnation of mobility. 31
Our measure of intergenerational mobility just takes years of education, without any corrections for some
“quality” factor that may be important. Thus, a year in a PI or a TFC is equivalent to a year of university
according to our measure.
22
On the demand side, there are differences in the results whether we use university or total
enrollment. The results are also different to those in table 4, where we tested each
hypothesis alone. The only case in which permanent income is strongly significant is when
only permanent income at birth is included together with university enrollment. That is
also the estimation that explains more of the variance of intergenerational mobility.
The main conclusions on the demand side are two. First, permanent incomes at birth can
explain a part of the reduction that supply cannot. In the previous paragraph we saw that
universities supply can account for 86% of the reduction. The growth in our measure of
permanent income at birth was 28.6 (thousands) 1996 Chilean pesos. Using the coefficient
in column 1, table 5, we can see that the share of the reduction explained by income is a
12%, which leaves a (relatively insignificant) 2% unexplained. Second, permanent income
at age 18 is no longer important after including supply. The coefficient is no longer
statistically significant (the p-value is 11%) in column two, neither it is in column 3, where
the three hypotheses compete. Only supply and long-run credit constraints “survive”32
.
Thus, we find that permanent income at birth, which is a rough measure of the capacity of
parents to provide their offspring of abilities and human capital in the early stages of life,
and higher education supply, which at first was rapidly expanding but then suddenly
stopped, are the factors behind the large improvement in intergenerational mobility of
education measured by cohorts and the posterior stagnation.
To substantiate our results we can analyze whether access to tertiary education was
effectively the main channel through which mobility stagnated. Following literature for
developed countries (see Carneiro and Heckman (2002) and d‟Addio (2007)) we examine
the evolution of coverage of tertiary education for different groups, in terms of parent‟s
education.
VII. The Main Channel: Educational attainment of children according to parents’
attainment
VII.1. Absolute coverage
32
Table 12 shows the results using logs in both dependent and independent variables (panel A) and defining
permanent incomes as 5 years average instead of 10 (panel B). Results are not very different from those
discussed in the text.
23
We define four educational levels and divide the sample according to the higher level they
attained. Then, we estimate how many individuals in a specific cohort end up in each of
these educational levels. The four categories are: those we will say have incomplete
primary (one year of education or more); those that we will say have incomplete secondary
(7 years of education or more), those that have complete secondary (12 years of education
or more); and finally those that have incomplete tertiary (13 years of education or more)33
.
It is important to note that the different categories are not mutually exclusive. An individual
who belongs to complete secondary will also belong to the two previous levels, incomplete
secondary and incomplete primary. We now discuss the educational attainment of children
from parents in each category (that can be seen in figures 5 to 9).
What first strikes when looking at figure 5 is the fact that attainment has grown for all the
population. The percentage having at least one year of education grows from 89% to 99%
of the population. Coverage of incomplete secondary grows from 29% for the cohort born
in 1930 to 92% for the cohort born in 1978. Coverage of complete secondary also grows
substantially (from 18% to 67%). That is, two thirds of the population of the last cohort we
study had at least complete secondary. The percentage of the population that has at least
one year of tertiary education also grows sharply: from 7% to 28%.
These percentages first grow sharply and then much more moderately. In the first stage the
rates of growth of coverage are: 0.3%, 3.6%, 3.5% and 3.1% for the four educational levels.
In the second stage (1958-78) these percentages drop to 0%, 0.9%, 2% and 2.9%. The only
rate of expansion that is not substantially lower and actually is similar in both stages is that
for tertiary coverage (3.1% vs. 2.9%). Hence it does not appear that tertiary education
coverage is at issue. Surely it cannot explain the stagnation of mobility if it continued to
grow at similar levels as before.
To better understand the evolution of coverage we look at children‟s coverage according to
their parents‟ educational attainment. We classify them in overlapping groups (children are
present in the highest educational category they achieved and in all previous educational
categories). Parental coverage is classified into non overlapping categories: they are
included only in the highest educational level they achieve. For example, a child that has
33
Although the group is labeled as “incomplete” it includes people with complete higher education.
24
some tertiary education, of a parent with complete secondary, will be part of the group of
children from parents with complete secondary, though he will appear in all the educational
categories within this group: incomplete primary, incomplete secondary, complete
secondary and incomplete tertiary.
Table 8 shows the percentage of parents that belong to each group for the respective
cohorts, defined as the year of birth of their sons. We make this classification to pay
attention to the question whether the increase in coverage in children we described earlier is
due to (i) an increase in coverage independent of the education of the parents, (ii) an
increase in coverage only for children of parents with higher education levels, or (iii) an
increase in coverage due only to an increase in parents‟ education, but with the probability
of coverage unchanged once one controls for parents education.
VII.2. Coverage according to parents‟ attainment
Coverage of incomplete primary increases for children of parents with all education levels,
converging to 100% for all groups. Hence we can say that the probability of having at least
one year of education is independent of family background. We also observe a strong
tendency to both increase and converge for coverage of incomplete secondary, independent
of parent‟s education. The convergence is complete for children of parents with 7-11, 12
and 13+ years of education. However, even though convergence is strong for children of
parents with 1-6 years of education for the cohort born in 1978 there still is a large gap in
coverage. In numbers, the level of coverage for the children of parents with the three higher
levels of education (7+ years of education) converges to 98%. For the children of parents
with 1-6 years of education the level of coverage reached for the cohort born in 1978 is
84%34
. The evolution of the coverage of incomplete primary and incomplete secondary are
shown in figures 6 and 7 respectively.
For the evolution of the coverage of complete secondary we start seeing noticeable
differences in how coverage evolves for children with different parental educational levels.
In particular, we can see a lack of convergence (see figure 6). In figure 5 we see that
coverage grows, though when we look at it conditional on parental education (figure 8)
34
The group of parents with 1-6 years of education substantially decreases in numbers throughout the period
under analysis. Hence the children in this situation are a small percentage of the total.
25
then coverage for the four groups rises almost in parallel. However, there is some
convergence before 1957. Coverage grows at rates of 4.6%, 3%, 1.2% and 1.5% (for the
four educational levels, ordered from less to more education) showing a negative
relationship between coverage growth and parental education that justifies the existence of
convergence. In the second stage, for cohorts born between 1958 and 1978, the coverage
differences by parental education tend to persist (or to close the gap much more slowly).
Coverage grows at rates of 1.8%, 0.3%, 1.1% and 0.2%.
Finally, we analyze coverage in incomplete tertiary education. This is possibly the most
interesting of all the tendencies we have analyzed and confirm the results from the previous
section. In figure 9 we do not see convergence but divergence (or stability followed by
divergence). Coverage for children of parents with 1-6 years of education grows very
slowly during the whole period, from 5% to 10%. Coverage for children of parents with 7-
11 years of education grows form 14% to 33% and for those children of parents with 12
years it grows from 7% to 51%. The first two coverage rates double but the third triples.
For children with parents with 13+ years of education the rate also more than doubles, from
37% to 81%. But possibly the most interesting difference does not occur from start to finish
of the period under study, but in the second stage we have identified (i.e. cohorts born after
1957). In this second stage the rate of growth of coverage for the four levels of parental
education are: 0.0%, 1.2%, 2.6% and 1.0%, showing divergence. The growth of coverage
during the first stage had been of 3.1%, 2.7%, 2.0% and 2.3%, showing a small degree of
convergence.
If one compares these rates of change, one thing stands out: the relatively large increase in
tertiary coverage for the children of parents with complete secondary. That is a key
ingredient in the divergence between this group and the children of parents with lower than
complete secondary. The stagnation of tertiary education supply is probably at fault here. If
rationing of vacancies occurs according to the results of the academic aptitude test, which
in turn is correlated to education quality and permanent income, then the reduction in
enrollment hurts children of less educated parents more, a phenomena that is reflected in
the relative divergence in tertiary education coverage for different groups in figure 9.
26
In sum, two main conclusions about the relationship between intergenerational mobility and
educational attainment can be drawn. First, when mobility increased for cohorts born
between 1930 and 1957 there was a large expansion in the share of each cohort that
completed primary and secondary education, which can be seen in the evolution of the first
three groups we previously defined (figures 6 to 8). This was not the case for coverage of
tertiary education (figure 9), which was relatively stagnant throughout our sample. Second,
when mobility stagnated for cohorts born in 1958 onwards educational coverage still grew.
The stagnation in mobility was due to differences in the evolution of coverage for children
of parents with different educational levels. Children of less educated parents were not able
to achieve higher levels of education, while children from more educated parents did
achieve those levels.
VIII. Conclusions
Economic and social development in Chile during the twentieth century brought advances
in a broad range of institutions, including education. While cohorts born in 1930 had (on
average) 6 years of schooling, those born in the late seventies reached almost complete
secondary education (12 years). This improvement was accompanied by an increase in the
intergenerational mobility of education, measured by the correlation between the
educational level reached by a child and the one achieved by his parent.
Intergenerational mobility greatly improved in Chile for cohorts born during the first half of
the century. The correlation between parents and children education declined from 0.67 for
those born in 1930 (a level comparable with other relatively immobile Latin American
countries) to 0.41 for the cohort born in 1957 (which is comparable to that of some
developed countries). But starting with the generation born in 1958 mobility faced a sudden
stop and stagnated. It barely changed from this generation to those born in 1978, where the
correlation was still 0.41.
We find that both the demand and the supply of education played a major role in the
evolution of mobility. On the one side long-run credit constraints began to be relevant for
cohorts born after 1956. On the other, after the change of government in 1973 the supply of
27
vacancies in tertiary education was sharply reduced and then frozen, preventing many
teenagers of achieving higher educational levels. If one assumes that the entrance to
university is ordered according to ability (this means that the more skilled group enter first,
then the second, third, etc.), again, the children of less educated parents are the most hurt.
Hence following long-run credit constraints, which handicapped them on their early
childhood, they were faced with supply constraints.
The combination of credit constraints and stagnated supply are bad for mobility. However,
if we had access to newer data (cohorts born after 1978) we expect to see that these factors
have been attenuated or removed. On the one hand economic growth has increased
permanent incomes for new families, thus we should observe a lower percentage of
children with binding credit constraints. On the other hand, as can be seen in figure 3, in
1990 the university supply of vacancies began to grow sharply again. Hence those that were
teenagers in the nineties had more possibilities to access tertiary education than their
parents. Moreover there are institutions offering vacancies that do not ration according to
the aptitude test, hence making entrance less conditional on previous restrictions. We
expect these developments will result in an improvement in intergenerational mobility.
28
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30
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31
Appendix 1. Alternative explanations
A1.1. Family structure
A hypothesis that is related to long term credit constraints argues that family structure; specifically
single-parent families (SPF) affect human capital accumulation by children. Recent work has found
that (for the US) SPF are associated with higher levels of high school drop-out rates and teenage
pregnancy, and have lower results in standardized test scores (see McLanahan and Sandefur (1994),
Deleire and Kalil (2002)). Figure A1 plots the fraction of SPF by cohort in our sample. The pattern
is highly similar to the evolution of intergenerational mobility (figure 2), and shows that for older
cohorts the fraction of SPF is relatively high, though it falls sharply for cohorts born during the
forties and fifties from a value of 17.5% for the cohort born in 1931 to 6.9% for those born in 1957,
implying an average reduction of 2.16% per year35
. After the cohort born in 1957 the fraction of
SPF stagnates, which can be seen in figure 2, where for cohorts born between 1958 and 1978 the
value raises an average of 0.003 per year (0.3%) which can be thought as a sign of stagnation (at
least relative to the high reduction seen in the first period). Thus we have that the fraction of single
parent families shows an evolution very similar to intergenerational mobility, and other empirical
evidence tell us that SPF are associated with lower educational achievement. To test this, table A1
shows the results of a regression of the correlation of child and parent educational levels and the
fraction of SPF, and also includes the other hypotheses. SPF presents a statistically significant
coefficient, implying that as the number of SPF fell, the coefficient of correlation also fell, hence
the reduction in SPF contributed to the increase in mobility. But, as it can be seen in tables A2 and
A3, if we estimate this regressions separately for families whose parents have 0 to 6 years of
education and for families whose parents have 7 to 11 (there aren´t SPF whose parents have more
than 11 years of education), the SPF hypothesis only is statistically significant in the second group
of families, which for almost all the cohorts the number of SPF is 0 (the total percentage of SPF
comes almost exclusively from the first group), indicating that SPF has no explicative power over
intergenerational mobility and rejecting family structure hypothesis.
Figure A1: Fraction of single parent families for each cohort
35
Although the values are highly unstable the dashed line in figure 9 shows the (quadratic) fitted values of the
fraction of single parent families, which shows a sustained reduction in spite of the high variation of
point values for a particular cohort.
.05
.1.1
5.2
Fra
ctio
n
1930 1940 1950 1960 1970 1980Year of Birth
Fraction of single parent families Fitted values
32
Table A1: The effect of Single-parent Families on intergenerational mobility
(1) (2) (3) (4) (5) (6)
SFP 1.838*** 1.337*** 0.680** 0.652** 0.631** 0.664**
[0.214] [0.252] [0.265] [0.257] [0.249] [0.253]
Universities -0.000935*** -0.000811*** -0.000928***
[0.000155] [0.000154] [0.000236]
Income at birth -0.00288*** -0.000137 -0.00103*** -0.00132**
[0.000625] [0.000591] [0.000325] [0.000531]
Income at age 18 -0.00268*** 0.000548
[0.000557] [0.000791]
Observations 49 49 49 49 49 49
R-squared 0.390 0.574 0.707 0.756 0.773 0.774
Notes: Notes: OLS regressions, the dependent variable is intergenerational mobility of education by cohort (results from
table 2). Columns 1 tests the SPF hypothesis alone; columns 2 to 6 add the credit constraints and supply hypotheses
combined using universities supply. All incomes in 1996 thousand of Chilean pesos. Robust standard errors in brackets.
*** p<0.01, ** p<0.05, * p<0.1
Table A2: The effect of Single-parent families on intergenerational mobility in families with parents with 0 to 6 years
education
(1) (2) (3) (4) (5) (6)
SFP 0a6 0.589 0.630** 0.284 0.255 0.377 0.479*
[0.477] [0.278] [0.272] [0.269] [0.231] [0.258]
Income at birth -0.00656*** -0.00245 -0.00345*** -0.00462**
[0.000981] [0.00156] [0.000962] [0.00173]
Income at age 18 -0.00335*** 0.00205
[0.00101] [0.00216]
universidades -0.00149*** -0.00104*** -0.00149***
[0.000173] [0.000196] [0.000450]
Observations 49 49 49 49 49 49
R-squared 0.037 0.523 0.633 0.615 0.698 0.706
Notes: OLS regressions, the dependent variable is intergenerational mobility of education by cohort for families with
parents with 0 to 6 years of education. Column 1 test de SPF hypothesis alone; columns 2 to 6 add the credit constrains
and supply hypotheses combined using university supply. All incomes in 1996 thousand of Chilean pesos.
Robust standard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1
Table A3: The effect of Single-parent families on intergenerational mobility in families with parents with 7 to 11 years
education
(1) (2) (3) (4) (5) (6)
SFP 7a11 -3.582*** -3.241** -2.966** -2.894** -2.884** -2.884**
[1.160] [1.208] [1.219] [1.242] [1.261] [1.278]
Income at birth 0.00422 -5.57e-05 0.00119 0.00138
[0.00270] [0.00303] [0.00210] [0.00411]
Income at age 18 0.00356 -0.000350
[0.00251] [0.00524]
universidades 0.00120* 0.00105 0.00113
[0.000683] [0.000669] [0.00141]
Observations 49 49 49 49 49 49
R-squared 0.080 0.120 0.147 0.154 0.156 0.156
Notes: OLS regressions, the dependent variable is intergenerational mobility of education by cohort for families with
parents with 7 to 11 years of education. Column 1 test de SPF hypothesis alone; columns 2 to 6 add the credit constrains
and supply hypotheses combined using university supply. All incomes in 1996 thousand of Chilean pesos.
Robust standard errors in brackets. *** p<0.01, ** p<0.05, * p<0.1
33
A1.2. Mandatory schooling laws
Four laws increasing the level of mandatory education have been approved in the relevant period
(i.e. affecting the cohorts we examine). The laws were approved in 1920 (imposing a 4 year
minimum), 1929 (6 year minimum) and 1965 (8 year minimum)36
. To analyze the effect of these
four laws on the evolution of mobility we concentrate on whether they have had an impact on the
coverage percentages by cohort. We look at this through two different tests.
First, we look at the percentage of coverage for each cohort that should abide by the mandatory
minimum. Then we do a regression of this coverage and see whether the approval of the law
significantly changes the evolution of coverage. We do this analysis to test the effect of the 1965
law since this is the law we have more data for.
Before we proceed with the analyses, it is useful to briefly discuss which cohort will be considered
affected by the laws. The laws affect the children in the level immediately preceding the level that
becomes mandatory. For example, the law that mandates a minimum of 6 years of schooling affects
those that are in the fifth year of primary school, who would not be able to choose whether to
continue or not the next year. Since this law was approved in 1929, it affected those that were in
fifth year of primary school at the time. That is, it affects those that where 11 years old in 1929,
hence those born in 1918. To generalize, a law approved the year X that mandates level S of
schooling will affect those that are 6+(S-1) years old; therefore the first cohort affected is that born
in year Y, where year Y is estimated as X - (S-1) – 6, or X - S – 5. The number six introduced in the
formula comes from the age of entry to primary school. This formula tells us then that the 1920 year
law with a 4 year minimum affected all cohorts that where born from 1911 onwards; the 1929 law,
those born from 1918 on and the 1965 law those born from 1952 on.
Percentage of each cohort that abides by the mandatory minimum
We concentrate on the effects of the 8 year minimum imposed on the 1952 cohort. The evolution of
the percentage of individuals of each cohort that meet the minimum imposed regulation is shown in
figure A2. There is acceleration in the percentage that abides by the minimum, but that precedes
rather than follows the approval of the law. The graph illustrates a situation that we are able to test
empirically with a regression. We will do it only for the 1965 law that imposes an 8 year minimum,
since it is the law for which we have the most observations and the only one for which we have
observations both for cohorts not affected and cohorts affected by the law.
36
In 2003 a law imposing 12 years of minimum mandatory education was approved, but our data does not
allow us to study its effects, since the cohorts that were affected by it begin with those born in 1986 and our
data ends with the cohort of 1978.
34
Figure A2: Percentage of individuals the meet the minimum schooling, by
moment of promulgation of the law
Regression analysis
We test for changes in trend for the 1952 cohort and after. The results are shown in table A3. We
can see that the change in the trend of coverage after the law is in fact negative (column 1), which
tells us that the rate of growth falls after the 1952 cohort. A second empirical work looks for all
structural breaks and the analysis of the time series finds three structural breaks: for the cohorts
born in 1944, 1953 and 1957. Columns 2 through 4 in table A2 show the results. Again the trend
found after the imposition of the law (for columns 3 and 4) has a lower rate of growth than the trend
from before that cohort. In turn, in column 2 we propose a structural break before the imposition of
mandatory primary schooling, when the rate of growth was higher (see figure A2) and find that the
trend increased before the law was imposed (this last case serves as a falsification exercise).
Table A3: The effect of mandatory primary school law on the rate of growth of coverage
(1) (2) (3) (4)
1952 1944 1953 1957
Trend 0.0125*** 0.00816*** 0.0132*** 0.0165***
[0.00117] [0.00165] [0.00120] [0.00133]
TrendxReform -0.00296** 0.00606*** -0.00438*** -0.00860***
[0.00138] [0.00189] [0.00128] [0.00136]
Dummy Reform 0.210*** -0.00419 0.244*** 0.310***
[0.0327] [0.0358] [0.0241] [0.0235]
Observations 49 49 49 49
R-squared 0.987 0.962 0.988 0.976
Notes: OLS regressions, the dependent variable is intergenerational mobility of education by cohort
(results from table 2). All columns test for a structural break in the evolution of intergenerational
mobility. Column 1 tests it in 1952, column 2 in 1944, column 3 in 1953 and column 4 in 1957. The
independent variables are a constant, a time trend, a dummy that takes the value 1 after the respective
year, and the interaction of the trend and the dummy. Robust standard errors in brackets. *** p<0.01, **
p<0.05, * p<0.1
0.2
.4.6
.81
Fra
ctio
n
1930 1940 1950 1960 1970 1980Year of Birth
35
What these results tell us is that a policy that was supposed to improve mobility does not. We could
have expected that the law would have forced children from less educated parents to achieve a
higher level of education than they would have otherwise reached, improving levels of mobility.
Instead we see the reverse effect. However the conclusion should be that the law has no effect. The
results we find must not be taken as a causal effect, we do not expect that mandatory educational
laws reduce the growth of coverage.
Event study
We use a second methodology to study whether the laws has an effect on the trend of coverage, that
is, event studies. This methodology is used in finance to study the impact of news, for example, on
the value of a stock (McKinlay (1997)). Here we use the method to study the impact of the law on
the time series of eight year coverage by cohort. We fit a trend to the trajectory of the variable
before the event and test whether the true trajectory after the event deviates from the projection of
the time trend followed before the event. Since the percentage of persons with at least eight years of
schooling in a cohort is bound by 0 and 100 we fit a lognormal, transforming the dependent variable
through a logistic function ( ( ⁄ ). This transformation guarantees that the estimated
trajectory will converge to 100%. Thought, we are testing whether the law accelerated the
convergence with respect to the trend followed before the approval of the law.
We estimate the log normal function ( ( ⁄ ) . Where X is the
percentage of individuals in a cohort that have at least eight years of education, and T is simply a
trend. We estimate this function for cohorts born between 1930 and 1951 (before the event) so as
not to contaminate the trend with the event (this is standard practice). With this estimate we predict
the percentage of coverage for the rest of the period 1952- 1978. We then estimate the prediction
error for each cohort (the difference between the prediction and the realization). We test then
whether the accumulation of errors is significantly different from zero. The results can be seen in
table A4 and figure A3.
After the cohort born in 1956 there is a significant deviation from the projected trend but it is not
because the realized trend accelerated; the trend actually decelerated after the law. Hence we reject
that the laws had any effect in the acceleration of intergenerational mobility, and so the lack of new
laws does not explain the stagnation of mobility in the most recent cohorts.
36
Table A4 Event Study: Impact of mandatory primary education law over the percentage of individuals with 8 or more years of schooling
Cohort Distance from the Event % cohort with 8+ years of schooling Prediction Error Cumulate Error Test
1930 -22 28.10% 29.48% -1.38% -1.38%
1931 -21 30.60% 29.47% 1.13% -0.24%
1932 -20 31.90% 29.65% 2.25% 2.01% 1933 -19 30.20% 29.99% 0.21% 2.22%
1934 -18 26.60% 30.48% -3.88% -1.66% 1935 -17 33.50% 31.08% 2.42% 0.76%
1936 -16 31.40% 31.79% -0.39% 0.37%
1937 -15 31.10% 32.59% -1.49% -1.12%
1938 -14 36.00% 33.47% 2.53% 1.41%
1939 -13 33.80% 34.43% -0.63% 0.78% 1940 -12 31.70% 35.47% -3.77% -2.99%
1941 -11 40.80% 36.60% 4.20% 1.21% 1942 -10 36.70% 37.82% -1.12% 0.08%
1943 -9 41.20% 39.15% 2.05% 2.13%
1944 -8 39.30% 40.61% -1.31% 0.82% 1945 -7 42.30% 42.23% 0.07% 0.89%
1946 -6 43.70% 44.02% -0.32% 0.57% 1947 -5 46.60% 46.04% 0.56% 1.13%
1948 -4 48.00% 48.31% -0.31% 0.82%
1949 -3 49.90% 50.87% -0.97% -0.15%
1950 -2 54.30% 53.77% 0.53% 0.38%
1951 -1 57.20% 57.02% 0.18% 0.56% 1952 0 59.60% 60.64% -1.04% -0.48% -0.469
1953 1 66.90% 64.63% 2.27% 1.79% 0.391
1954 2 66.20% 68.92% -2.72% -0.93% -0.386
1955 3 71.60% 73.43% -1.83% -2.75% -0.744
1956 4 70.90% 78.00% -7.10% -9.86% -2.094
1957 5 74.90% 82.47% -7.57% -17.43% -3.301
1958 6 74.10% 86.62% -12.52% -29.95% -5.183
1959 7 75.30% 90.27% -14.97% -44.91% -7.227
1960 8 76.00% 93.29% -17.29% -62.20% -9.404
1961 9 79.00% 95.62% -16.62% -78.82% -11.284
1962 10 77.40% 97.31% -19.91% -98.74% -13.458
1963 11 78.50% 98.45% -19.95% -118.69% -15.474
1964 12 77.30% 99.17% -21.87% -140.56% -17.593
1965 13 79.60% 99.58% -19.98% -160.54% -19.354
1966 14 79.80% 99.81% -20.01% -180.55% -21.020
1967 15 81.30% 99.92% -18.62% -199.16% -22.444
1968 16 82.30% 99.97% -17.67% -216.83% -23.700
1969 17 84.50% 99.99% -15.49% -232.32% -24.673
1970 18 83.50% 100.00% -16.50% -248.81% -25.717
1971 19 86.10% 100.00% -13.90% -262.71% -26.462
1972 20 84.80% 100.00% -15.20% -277.91% -27.316
1973 21 86.60% 100.00% -13.40% -291.31% -27.972
1974 22 87.40% 100.00% -12.60% -303.91% -28.538
1975 23 88.90% 100.00% -11.10% -315.01% -28.956
1976 24 89.40% 100.00% -10.60% -325.61% -29.324
1977 25 90.00% 100.00% -10.00% -335.61% -29.636
1978 26 89.30% 100.00% -10.70% -346.31% -30.007
37
Figure A3: Event Study: Impact of mandatory primary education law over the percentage of
individuals with 8 or more years of schooling
.2.4
.6.8
1
Per
centa
ge
1930 1940 1950 1960 1970 1980Year of Birth
% cohort with 8 or more years of schooling Prediction
38
Additional References Cited in the Appendices
Björklud, A. and M. Jäntti (1997), “Intergenerational Income Mobility in Sweden Compared to the United
States”, The American Economic Review 87(5), pp. 1009-1018.
Deleire, T. and A. Kalil (2002), “Good Things Come in Threes: Single-Parent Multigenerational Family
Structure and Adolescent Adjustment,” Demography, Vol. 39 No.2, pp.393-413.
MacKinley, A. C. (1997), “Event Studies in Economics and Finance”, Journal of Economic Literature, Vol.
35(1) pp.13-39
McLanahan, S. y G. D. Sandefur (1994), Growing Up with a Single Parent: What Hurts, What Helps,
Cambridge, MA: Harvard University Press.
Solon, G. (1992), “Intergenerational Income Mobility in the United States”, The American Economic Review
82(3), pp. 393-408.
39
Tables
Table 1: Summary statistics for available data by cohort (year of birth)
Cohort N Child Mean Schooling Father's Mean Schooling
1930 427 6.04 4.50
1931 304 6.08 4.68
1932 527 6.30 4.62
1933 321 6.11 4.40
1934 564 5.84 4.19
1935 460 6.48 4.55
1936 513 6.29 4.51
1937 687 6.28 4.29
1938 580 6.63 4.42
1939 692 6.55 4.39
1940 805 6.49 4.08
1941 588 7.13 4.70
1942 1,119 6.98 4.67
1943 725 7.18 4.97
1944 1,19 7.20 4.78
1945 879 7.31 4.73
1946 1,063 7.54 4.79
1947 1,141 7.83 4.89
1948 1,233 7.89 4.99
1949 1,087 8.15 4.94
1950 1,572 8.44 5.21
1951 1,112 8.71 5.41
1952 1,927 8.82 5.15
1953 1,352 9.31 5.44
1954 2,110 9.15 5.21
1955 1,596 9.60 5.65
1956 1,912 9.42 5.36
1957 2,114 9.88 5.74
1958 1,932 9.76 5.65
1959 2,030 9.70 5.54
1960 2,444 9.79 5.69
1961 1,899 10.19 6.09
1962 2,883 9.93 5.72
1963 2,288 10.13 6.04
1964 2,825 10.04 5.81
1965 2,332 10.12 5.99
1966 2,459 10.26 6.12
1967 2,364 10.37 6.09
1968 2,123 10.51 6.28
1969 2,098 10.82 6.54
1970 2,255 10.72 6.58
1971 1,814 11.05 6.97
1972 2,471 10.94 6.97
1973 1,976 11.32 7.25
1974 2,135 11.29 7.30
1975 1,892 11.47 7.58
1976 1,804 11.55 7.75
1977 1,691 11.71 8.04
1978 1,605 11.57 8.20
Total 73,920
Data was obtained using the 2002 and 2004 versions of the EPS. The column cohort refers to the year of birth of the child. Child‟s Mean schooling
refers to the average years of education of the corresponding cohort, while Parent‟s mean schooling refers to the average years of education of the
fathers of each cohort, those parents may have been born in different years, we do not separate them.
40
Table 2: Correlation between child and parent education (in levels)
Father‟s education × cohort
Father‟s education × cohort
F.E.×1930 0.668***
F.E.×1955 0.438***
F.E.×1931 0.619***
F.E.×1956 0.476***
F.E.×1932 0.615***
F.E.×1957 0.407***
F.E.×1933 0.651***
F.E.×1958 0.443***
F.E.×1934 0.551***
F.E.×1959 0.423***
F.E.×1935 0.557***
F.E.×1960 0.426***
F.E.×1936 0.564***
F.E.×1961 0.407***
F.E.×1937 0.558***
F.E.×1962 0.435***
F.E.×1938 0.609***
F.E.×1963 0.402***
F.E.×1939 0.598***
F.E.×1964 0.413***
F.E.×1940 0.645***
F.E.×1965 0.404***
F.E.×1941 0.533***
F.E.×1966 0.426***
F.E.×1942 0.539***
F.E.×1967 0.420***
F.E.×1943 0.518***
F.E.×1968 0.407***
F.E.×1944 0.534***
F.E.×1969 0.409***
F.E.×1945 0.502***
F.E.×1970 0.408***
F.E.×1946 0.494***
F.E.×1971 0.396***
F.E.×1947 0.491***
F.E.×1972 0.411***
F.E.×1948 0.508***
F.E.×1973 0.430***
F.E.×1949 0.536***
F.E.×1974 0.402***
F.E.×1950 0.521***
F.E.×1975 0.357***
F.E.×1951 0.481***
F.E.×1976 0.397***
F.E.×1952 0.502***
F.E.×1977 0.401***
F.E.×1953 0.483***
F.E.×1978 0.406***
F.E.×1954 0.495***
Observations 63,445
R-squared 0.3406
Notes: The table shows the coefficient of a regression of child
education on parent education, by cohorts (see equation (12)). The
regression includes a constant a full set of dummies by cohort. Robust
standard errors, clustered by cohort not reported. All coefficients are
significant at the 1% level.
41
Table 3: Correlation between child and parent education (in logs)
Father‟s education × cohort
Father‟s education × cohort
LN(F.E.)×1930 0.641***
LN(F.E.)×1955 0.245***
LN(F.E.)×1931 0.514***
LN(F.E.)×1956 0.272***
LN(F.E.)×1932 0.532***
LN(F.E.)×1957 0.238***
LN(F.E.)×1933 0.549***
LN(F.E.)×1958 0.288***
LN(F.E.)×1934 0.500***
LN(F.E.)×1959 0.254***
LN(F.E.)×1935 0.527***
LN(F.E.)×1960 0.255***
LN(F.E.)×1936 0.533***
LN(F.E.)×1961 0.221***
LN(F.E.)×1937 0.407***
LN(F.E.)×1962 0.260***
LN(F.E.)×1938 0.448***
LN(F.E.)×1963 0.250***
LN(F.E.)×1939 0.444***
LN(F.E.)×1964 0.255***
LN(F.E.)×1940 0.486***
LN(F.E.)×1965 0.236***
LN(F.E.)×1941 0.445***
LN(F.E.)×1966 0.262***
LN(F.E.)×1942 0.410***
LN(F.E.)×1967 0.223***
LN(F.E.)×1943 0.458***
LN(F.E.)×1968 0.232***
LN(F.E.)×1944 0.415***
LN(F.E.)×1969 0.238***
LN(F.E.)×1945 0.386***
LN(F.E.)×1970 0.226***
LN(F.E.)×1946 0.367***
LN(F.E.)×1971 0.231***
LN(F.E.)×1947 0.336***
LN(F.E.)×1972 0.250***
LN(F.E.)×1948 0.364***
LN(F.E.)×1973 0.245***
LN(F.E.)×1949 0.361***
LN(F.E.)×1974 0.251***
LN(F.E.)×1950 0.359***
LN(F.E.)×1975 0.234***
LN(F.E.)×1951 0.325***
LN(F.E.)×1976 0.248***
LN(F.E.)×1952 0.368***
LN(F.E.)×1977 0.247***
LN(F.E.)×1953 0.292***
LN(F.E.)×1978 0.252***
LN(F.E.)×1954 0.287***
Observations 51,963
R-squared 0.2618 Notes: The table shows the coefficient of a regression of (log) child
education on (log) parent education, by cohorts (see equation (12)). The
regression includes a constant a full set of dummies by cohort. Robust
standard errors, clustered by cohort not reported. All coefficients are
significant at the 1% level.
42
Table 5: The separate effect of credit constraints and tertiary education on intergenerational mobility of education
(1) (2) (3) (4) (5) (6)
Income at birth -0.00109*** -0.00105* 0.00121 0.00111
[0.000394] [0.000607] [0.000761] [0.000760]
Income at age 18 -0.00100 -7.38e-05 -0.00141* -0.00129
[0.000611] [0.000881] [0.000746] [0.000801]
Universities -0.000956*** -0.000796*** -0.000939***
[0.000141] [0.000239] [0.000265]
Total Supply -0.000786*** -0.000390** -0.000531**
[0.000136] [0.000157] [0.000223]
Observations 49 49 49 49 49 49
R-squared 0.741 0.732 0.741 0.694 0.694 0.704
Notes: OLS regressions, the dependent variable is intergenerational mobility of education by cohort (results from table
2). Columns 1 to 3 test the credit constraints and supply hypotheses combined using universities supply. The
independent variables are a constant, low-skilled workers income at the moment of birth (col. 1), at age 18 (col. 2)
and both (col. 3). All incomes in 1996 thousand of Chilean pesos. Columns 4 to 6 test the credit constraints and
stagnated supply hypotheses using total tertiary education. Column 4 uses low-skilled workers income at the moment
of birth, column 5 income at age 18, and column 6 uses both. Robust standard errors in brackets. *** p<0.01, **
p<0.05, * p<0.1
Table 4: The separate effect of credit constraints and tertiary
education on intergenerational mobility of education
(1) (2) (3)
Panel A: Credit Constraints Hypothesis
Income at birth -0.00393*** 0.000154
[0.000574] [0.000664]
Income at age 18 -0.00327*** -0.00335***
[0.000302] [0.000503]
Observations 49 49 49
R-squared 0.395 0.672 0.672
Panel B: Stagnated Supply Hypothesis
Universities -0.00109*** -0.00105***
[0.000128] [0.000134]
Total Supply -0.000657***
[7.22e-05]
IP 0.00162
[0.00243]
TFC -0.00101
[0.00127]
Observations 49 49 46
R-squared 0.722 0.683 0.734
Notes: OLS regressions, in both panels the dependent variable is
intergenerational mobility of education by cohort (results from
table 2). Panel A tests the credit constraints hypothesis. The
independent variables are a constant, low-skilled workers income
at the moment of birth (col. 1), at age 18 (col. 2) and both (col. 3).
All incomes in 1996 thousand of Chilean pesos. Panel B tests the
stagnated supply hypothesis. Column 1 uses the universities
supply (in thousands), column 2 total tertiary education supply,
and column 3 uses a disaggregated measure of total supply, which
is separated in the three different segments of the market
(universities, IPs and TFCs). Robust standard errors in brackets.
*** p<0.01, ** p<0.05, * p<0.1
43
Table 8: percentage of parents on each educational group
Cohort
Parents with
0-6 years
Parents with
7-11 years
Parents with
12 years
Parents with 13
years or more
1930 0.79 0.08 0.11 0.02
1931 0.77 0.11 0.10 0.03
1932 0.78 0.07 0.12 0.03
1933 0.81 0.06 0.09 0.04
1934 0.79 0.07 0.12 0.02
1935 0.81 0.06 0.09 0.04
1936 0.79 0.07 0.12 0.03
1937 0.81 0.08 0.09 0.02
1938 0.81 0.07 0.09 0.03
1939 0.79 0.09 0.09 0.03
1940 0.83 0.07 0.08 0.02
1941 0.77 0.09 0.11 0.03
1942 0.78 0.10 0.09 0.03
1943 0.77 0.09 0.09 0.04
1944 0.77 0.12 0.09 0.03
1945 0.77 0.11 0.09 0.03
1946 0.76 0.10 0.10 0.03
1947 0.75 0.12 0.10 0.03
1948 0.75 0.11 0.10 0.04
1949 0.76 0.11 0.11 0.02
1950 0.74 0.12 0.10 0.04
1951 0.72 0.13 0.11 0.04
1952 0.73 0.12 0.11 0.04
1953 0.72 0.13 0.12 0.04
1954 0.73 0.13 0.11 0.03
1955 0.71 0.13 0.12 0.04
1956 0.72 0.14 0.11 0.03
1957 0.69 0.15 0.13 0.04
1958 0.70 0.15 0.12 0.04
1959 0.71 0.14 0.11 0.04
1960 0.70 0.14 0.12 0.04
1961 0.66 0.16 0.14 0.05
1962 0.69 0.15 0.13 0.04
1963 0.66 0.16 0.13 0.05
1964 0.68 0.15 0.13 0.04
1965 0.67 0.16 0.13 0.05
1966 0.65 0.17 0.13 0.05
1967 0.65 0.18 0.12 0.05
1968 0.63 0.19 0.12 0.06
1969 0.60 0.21 0.14 0.06
1970 0.60 0.20 0.13 0.06
1971 0.57 0.20 0.15 0.08
1972 0.57 0.20 0.16 0.08
1973 0.53 0.23 0.15 0.09
1974 0.53 0.23 0.17 0.08
1975 0.49 0.24 0.18 0.10
1976 0.46 0.27 0.17 0.10
1977 0.44 0.28 0.17 0.11
1978 0.42 0.28 0.19 0.11
44
Table 9: Robustness check using logs in dependent and independent variables
(1) (2) (3) (4) (5) (6)
Dep. Var. in levels Dep. Var. in logs
Ln(Income at birth) -0.255*** -0.0221 -0.326*** 0.0389
[0.0362] [0.0396] [0.0536] [0.0427]
Ln(Income at age 18) -0.241*** -0.229*** -0.337*** -0.358***
[0.0204] [0.0318] [0.0295] [0.0364]
Observations 49 49 49 49 49 49
R-squared 0.419 0.709 0.710 0.354 0.720 0.722
Notes: OLS regressions of intergenerational mobility of education on credit constraints. In columns 1 to 3 the dependent
variable is the regression coefficient of parents‟ years of education on children‟s years of education (results from table 2);
in columns 4 to 6 the dependent variable is the intergenerational mobility, defined as the regression coefficient of log
parent years of education on log child years of education (results from table 3). Columns 1 and 4 use permanent income
at birth, columns 2 and 5 use permanent income at age 18, columns 3 and 6 use both. Permanent income is defined as a
10 lagged years average of low-skilled wage from XXX. All incomes in 1996 thousand of Chilean pesos. Robust
standard error in brackets. *** p<0.01, ** p<0.05, * p<0.1
Table 10: Robustness check using alternative permanent incomes, and logs in
dependent and independent variables (1) (2) (3)
Panel A: Levels-Levels Income at birth -0.00250*** -0.000929***
[0.000451] [0.000294]
Income at age 18 -0.00240*** -0.00212***
[0.000327] [0.000325]
Observations 49 49 49
R-squared 0.231 0.532 0.557
Panel B: Levels-Logs Ln(Income at birth) -0.173*** -0.0553**
[0.0328] [0.0242]
Ln(Income at age 18) -0.180*** -0.161***
[0.0241] [0.0247]
Observations 49 49 49
R-squared 0.241 0.555 0.573
Panel C: Logs-Logs Ln(Income at birth) -0.232*** -0.0665**
[0.0485] [0.0315]
Ln(Income at age 18) -0.249*** -0.226***
[0.0332] [0.0312]
Observations 49 49 49
R-squared 0.223 0.546 0.560
Notes: OLS regressions of intergenerational mobility of education on credit
constraints. Panel A tests the credit constraints hypothesis using a level-level
approach. The dependent variable is the regression coefficient of parents‟ years of
education on children‟s years of education (results from table 2); independent
variables are measured in levels. Panel B also uses the results from table 2 as
dependent variable, though incomes are measured in logs. Panel C uses a level-logs
approach, the dependent variable is the intergenerational mobility, defined as the
regression coefficient of log parent years of education on log child years of education
(results from table 3). It also uses incomes in logs. Columns 1 uses permanent
income at birth, columns 2 uses permanent income at age 18, columns 3 uses both.
Permanent income is defined as a 5 lagged years average of low-skilled wage from
XXX. All incomes in 1996 thousand of Chilean pesos. Robust standard error in
brackets. *** p<0.01, ** p<0.05, * p<0.1.
45
Table 11: Robustness check using dependent variable and supply measured in logs
(1) (2) (3) (4)
Dep. Var. in levels Dep. Var. in logs
Ln(Universities) -0.0743*** -0.107***
[0.00485] [0.00594]
Ln(Total Supply) -0.0651*** -0.0923***
[0.00394] [0.00542]
Observations 49 49 49 49
R-squared 0.846 0.869 0.910 0.903
Notes: OLS regressions, columns 1 and 2 use the regression coefficient of parents‟ years of education on
children‟s years of education (results from table 2) as dependent variable, columns 3 and 4 use the regression
coefficient of log parent years of education on log child years of education (results from table 3) as dependent
variable. Columns 1 and 3 use the log universities supply (in thousands), column 2 and 4 use log total tertiary
education supply as independent variable. Robust standard error in brackets. *** p<0.01, ** p<0.05, * p<0.1.
Table 12: Robustness check for combined estimations
(1) (2) (3) (4) (5) (6)
Dep. Var. in levels Dep. Var. in logs
Panel A: 10 lags
Universities -0.0667*** -0.0729*** -0.0825*** -0.104*** -0.120*** -0.128***
[0.00593] [0.0115] [0.0126] [0.00626] [0.0131] [0.0135]
Income at birth -0.0629*** -0.0953*** -0.0259 -0.0744**
[0.0207] [0.0330] [0.0215] [0.0312]
Income at age 18 -0.00539 0.0764 0.0505 0.114*
[0.0399] [0.0582] [0.0453] [0.0574]
Observations 49 49 49 49 49 49
R-squared 0.863 0.846 0.871 0.912 0.913 0.921
Panel B: 5 lags
Universities -0.0691*** -0.0703*** -0.0712*** -0.101*** -0.109*** -0.110***
[0.00499] [0.00637] [0.00613] [0.00575] [0.00802] [0.00741]
Income at birth -0.0612*** -0.0643*** -0.0672*** -0.0805***
[0.0128] [0.0154] [0.0132] [0.0148]
Income at age 18 -0.0153 0.00870 0.00725 0.0373*
[0.0190] [0.0208] [0.0221] [0.0214]
Observations 49 49 49 49 49 49
R-squared 0.872 0.848 0.873 0.927 0.911 0.931
Notes: OLS regressions, columns 1 to 3 use the regression coefficient of parent‟s years of education on
children‟s years of education (results from table 2) as dependent variable, columns 4 to 6 use the regression
coefficient of log parent years of education on log child years of education (results from table 3) as dependent
variable. Panel A uses permanent incomes defined as the average of 10 years of incomes at birth and at 18.
Panel B uses permanent incomes defined as the average of 10 years of incomes at birth and at 18. Robust
standard error in brackets. *** p<0.01, ** p<0.05, * p<0.1.
46
Figures
Figure 1: Average years of schooling by cohorts
Figure 2: Intergenerational correlation of educational levels
46
81
01
2
Yea
rs o
f S
cho
oli
ng
1930 1940 1950 1960 1970 1980Year of Birth
Mean Education Children Mean Education Father
.3.4
.5.6
.7
1930 1940 1950 1960 1970 1980Year of Birth
47
Figure 3: Permanent income at birth and age 18.
Figure 4: Total tertiary education supply
40
60
80
10
01
20
Th
ou
san
ds
of
19
96
peso
s
1930 1940 1950 1960 1970 1980Year of Birth
Permanent Income at Birth Permanent Income at 18
0
10
02
00
30
04
00
Su
pp
ly (
tho
usa
nd
s)
1948 1956 1964 1972 1980 1988 1996Year
Total University
TFC PI
48
Figure 5: Absolute coverage for different educational levels
Figure 6: Coverage of incomplete primary according to parent‟s educational level
0.2
.4.6
.81
Co
ver
ag
e
1930 1940 1950 1960 1970 1980Year of Birth
1+ years 7+ years
12+ years 13+ years
0.2
.4.6
.81
Co
ver
age
1930 1940 1950 1960 1970 1980Year of Birth
1-6 years 7-11 years
12 years 13+ years
49
Figure 7: Coverage of incomplete secondary according to parent‟s educational level
Figure 8: Coverage of complete secondary according to parent‟s educational level
0.2
.4.6
.81
Co
ver
ag
e
1930 1940 1950 1960 1970 1980Year of Birth
1-6 years 7-11 years
12 years 13+ years
0.2
.4.6
.81
Co
ver
age
1930 1940 1950 1960 1970 1980Year of Birth
1-6 years 7-11 years
12 years 13+ years